Difference between revisions of "ApCoCoA-1:NC.IsHomog"
From ApCoCoAWiki
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<command> | <command> | ||
| − | <title> | + | <title>NCo.IsHomog</title> |
<short_description> | <short_description> | ||
| − | Check whether a polynomial | + | Check whether a polynomial or a list of polynomials is homogeneous in a non-commutative polynomial ring. |
</short_description> | </short_description> | ||
<syntax> | <syntax> | ||
| − | + | NCo.IsHomog(F:LIST):BOOL | |
</syntax> | </syntax> | ||
<description> | <description> | ||
<em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | <em>Please note:</em> The function(s) explained on this page is/are using the <em>ApCoCoAServer</em>. You will have to start the ApCoCoAServer in order to use it/them. | ||
<par/> | <par/> | ||
| − | Please set ring environment <em>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref> | + | Please set ring environment <em>coefficient field</em> <tt>K</tt>, <em>alphabet</em> (or set of indeterminates) <tt>X</tt> and <em>ordering</em> via the functions <ref>NCo.SetFp</ref>, <ref>NCo.SetX</ref> and <ref>NCo.SetOrdering</ref>, respectively, before calling the function. The default coefficient field is <tt>Q</tt>. The default ordering is length-lexicographic ordering (<quotes>LLEX</quotes>). For more information, please check the relevant functions. |
<itemize> | <itemize> | ||
<item>@param <em>F</em>: a polynomial or a LIST of polynomials in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | <item>@param <em>F</em>: a polynomial or a LIST of polynomials in <tt>K<X></tt>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <tt><X></tt> and C is the coefficient of W. For example, the polynomial <tt>F=xy-y+1</tt> is represented as F:=[[1,<quotes>xy</quotes>], [-1, <quotes>y</quotes>], [1,<quotes></quotes>]]. The zero polynomial <tt>0</tt> is represented as the empty LIST [].</item> | ||
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</itemize> | </itemize> | ||
<example> | <example> | ||
| − | + | NCo.SetX(<quotes>xy</quotes>); | |
F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; | F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; | ||
F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; | F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; | ||
F := [F1,F2]; | F := [F1,F2]; | ||
| − | + | NCo.IsHomog(F); | |
False | False | ||
------------------------------- | ------------------------------- | ||
| − | + | NCo.IsHomog(F1); | |
True | True | ||
------------------------------- | ------------------------------- | ||
| − | + | NCo.IsHomog(F2); | |
False | False | ||
------------------------------- | ------------------------------- | ||
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</description> | </description> | ||
<seealso> | <seealso> | ||
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<see>Introduction to CoCoAServer</see> | <see>Introduction to CoCoAServer</see> | ||
</seealso> | </seealso> | ||
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<type>non_commutative</type> | <type>non_commutative</type> | ||
</types> | </types> | ||
| − | <key> | + | <key>ncpoly.IsHomog</key> |
| − | <key> | + | <key>NCo.IsHomog</key> |
<key>IsHomog</key> | <key>IsHomog</key> | ||
| − | <wiki-category> | + | <wiki-category>Package_ncpoly</wiki-category> |
</command> | </command> | ||
Revision as of 17:20, 25 April 2013
NCo.IsHomog
Check whether a polynomial or a list of polynomials is homogeneous in a non-commutative polynomial ring.
Syntax
NCo.IsHomog(F:LIST):BOOL
Description
Please note: The function(s) explained on this page is/are using the ApCoCoAServer. You will have to start the ApCoCoAServer in order to use it/them.
Please set ring environment coefficient field K, alphabet (or set of indeterminates) X and ordering via the functions NCo.SetFp, NCo.SetX and NCo.SetOrdering, respectively, before calling the function. The default coefficient field is Q. The default ordering is length-lexicographic ordering ("LLEX"). For more information, please check the relevant functions.
@param F: a polynomial or a LIST of polynomials in K<X>. Each polynomial is represented as a LIST of monomials, which are pairs of the form [C, W] where W is a word in <X> and C is the coefficient of W. For example, the polynomial F=xy-y+1 is represented as F:=[[1,"xy"], [-1, "y"], [1,""]]. The zero polynomial 0 is represented as the empty LIST [].
@return: a BOOL value which is True if F is homogeneous and False otherwise. Note that if F is a set of homogeneous polynomials, then F generates a homogeneous ideal. It is false contrarily.
Example
NCo.SetX(<quotes>xy</quotes>); F1 := [[1,<quotes>x</quotes>], [1,<quotes>y</quotes>]]; F2 := [[1,<quotes>xx</quotes>],[1,<quotes>xy</quotes>],[1,<quotes>x</quotes>]]; F := [F1,F2]; NCo.IsHomog(F); False ------------------------------- NCo.IsHomog(F1); True ------------------------------- NCo.IsHomog(F2); False -------------------------------
See also
